The Reds found themselves 3-0 up at the Amex Stadium shortly after half-time thanks to an Emre Can goal and a Roberto Firmino double.
But Glenn Murray's 51st-minute penalty evoked memories of Liverpool's remarkable 3-3 draw at the Ramon Sanchez Pizjuan on November 21, when Sevilla battled back from 3-0 down.
Ultimately, Philippe Coutinho and a Lewis Dunk own goal wrapped things up for Liverpool late on, but Klopp acknowledged that he did have concerns when Brighton pulled one back.
A late Sevilla equaliser sees the points shared. pic.twitter.com/yol7DgXPOH— Liverpool FC (@LFC) November 21, 2017
"I would be lying if I said I didn't think 'yeah...' ," the German told reporters. "When you have it one time, unfortunately you need a little bit to get completely rid of this feeling.
"It's not that I thought it would happen 100 per cent. We were 2-0 up at half-time, made it 3-0 shortly after and usually that's it, especially how we scored it as well.
"They had a big chance, then we make a counter-attack and score – boom. That's really hard to cope with for the other team.
"Then they make it 3-1, and while the lead was not really insecure, it's not that I thought it could not happen, because a few weeks ago it happened.
"We needed this so we don't have the Sevilla game in our mind completely."
Klopp was particularly impressed with the performance of two-goal Firmino, praising his effectiveness at "annoying" Brighton.
Bobby's celebrations - a gift that keeps on giving! pic.twitter.com/pQ65SXNfY8— Liverpool FC (@LFC) December 2, 2017
"Roberto scored twice, but what he did around these goals is what excites me the most, to be honest," Klopp added.
"In all the counter-attacks, pretty much, he won the ball. By being here, by being a little annoying, a little foot, a little toe, that for us is important. Then the ball is go.
"With all the rest around him, you need to get used to it. They [the Liverpool players] are all different and all good.
"For me, I really like these players. That's why they are here."